Final answer:
The Declaration of Independence was indeed influenced by John Locke's theories , the Panic of 1819 led to decreased faith in the Second Bank of the United States , and the assertion about women's capabilities during war cannot be determined as true or false without additional context but historically women have taken on various roles during wartime.
Step-by-step explanation:
Exercise 8.1.1: The rationale that Jefferson used in the Declaration of Independence did indeed come primarily from the theories of John Locke, who believed in the concept of natural rights and that government should serve the people. Jefferson's argument for the colonies' separation from Britain was significantly influenced by Locke's philosophy on governance and social contract.
Exercise 12.1.2: The Panic of 1819 actually decreased the American people’s faith in the Second Bank of the United States due to issues surrounding speculation, lending, and a national financial crisis that it was unable to prevent or alleviate.
Exercise 8.3.2: The direct answer cannot be accurately determined without additional historical context from the period. However, it is important to note that during wartime, many women both historically and in contemporary times have often taken on additional roles and responsibilities, which demonstrates their capability in handling the burdens of war, contrary to the implication of the statement.